Question

Differential Equations

Use principle of superposition to find a particular solution

x^2y''- xy+y =2x^3

Answer #1

Differential Equations
(a) By inspection, find a particular solution of
y'' + 2y = 14.
yp(x)
= ______ANSWER HERE______.
(b) By inspection, find a particular solution of
y'' + 2y =
−4x.
yp(x)
= ______ANSWER HERE______
(c) Find a particular solution of y'' +
2y = −4x + 14.
yp(x)
= _____ANSWER HERE_____
(d) Find a particular solution of y'' +
2y = 8x + 7.
yp(x)
= ___ANSWER HERE____.

Find the solution of the Differential Equation
X^2y''-xy'+y=x

Find the differential Equation of
xy'-2y+(2x^3)e^-x=0

Find the particular solution of the differential equation: y "+ 2y
'+ y = 3x + 5 + 4e^-x

Find the solution to the linear system of differential
equations
{x′ = 6x + 4y
{y′=−2x
satisfying the initial conditions x(0)=−5 and
y(0)=−4.
x(t) = _____
y(t) = _____

Consider the system [ x' = -2y & y' = 2x] . Use dy/dx to
find the curves y = y(x).
Draw solution curves in the xy phase plane. What type of
equilibrium point is the origin?

Differential Equations problem
If y1= e^-x is a solution of the differential equation
y'''-y''+2y=0 . What is the general solution of the differential
equation?

Find a particular solution to each of the following differential
equations with the given initial condition:
A) dy/dx=ysinx/1+y^2, y(0)=1
B)dy/dx=xy ln x, y(1)=3
C)xy(1+x^2) dy/dx=(1+y^2), y(1)=0

Find the complete solution to the following differential
equations.
a) y''+2y'-y=10
b) 2y''- y = 3x^2

Verify that the function
y=x^2+c/x^2
is a solution of the differential equation
xy′+2y=4x^2, (x>0).
b) Find the value of c for which the solution satisfies the initial
condition y(4)=3.
c=

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